過去の記録

過去の記録 ~11/15本日 11/16 | 今後の予定 11/17~

2012年06月11日(月)

Kavli IPMU Komaba Seminar

16:30-18:00   数理科学研究科棟(駒場) 002号室
Changzheng Li 氏 (Kavli IPMU)
Quantum cohomology of flag varieties (ENGLISH)
[ 講演概要 ]
In this talk, I will give a brief introduction to the quantum cohomology of flag varieties first. Then I will introduce a Z^2-filtration on the quantum cohomology of complete flag varieties. In the end, we will study the quantum Pieri rules for complex/symplectic Grassmannians, as applications of the Z^2-filtration.

複素解析幾何セミナー

10:30-12:00   数理科学研究科棟(駒場) 126号室
Damian BROTBEK 氏 (University of Tokyo)
Differential forms on complete intersections (ENGLISH)
[ 講演概要 ]
Brückmann and Rackwitz proved a vanishing result for particular types of differential forms on complete intersection varieties. We will be interested in the cases not covered by their result. In some cases, we will show how the space $H^0(X,S^{m_1}\Omega_X\otimes \cdots \otimes S^{m_k}\Omega_X)$ depends on the equations defining $X$, and in particular we will prove that the theorem of Brückmann and Rackwitz is optimal. The proofs are based on simple, combinatorial, cohomology computations.

2012年06月09日(土)

調和解析駒場セミナー

13:30-17:00   数理科学研究科棟(駒場) 128号室
このセミナーは,月に1度程度,不定期に開催されます.
古谷康雄 氏 (東海大学

) 13:30-15:00
Cauchy積分に関する最近の話題(Muscaluらの仕事)
(JAPANESE)
[ 講演概要 ]
多重線形特異積分に関する Muscalu, Pipher, Tao, Thieleらの一連の仕事のほんの一部分を紹介する.キーワードはシンボル評価とshifted maximal function.
参考文献は Math. arXiv. に載っている Muscalu の三部作
岩渕 司 氏 (中央大学
) 15:30-17:00
Ill-posedness for the nonlinear Schr\\"odinger equations in one
space dimension
(JAPANESE)
[ 講演概要 ]
In this talk, we consider the Cauchy problems for the nonlinear Schr\\"odinger equations. In particular, we study the ill-posedness by showing that the continuous dependence on initial data does not hold. In the known results, Bejenaru-Tao (2006) considered the problem in the Sobolev spaces $H^s (\\mathbb R)$ and showed the ill-posedness when $s < -1 $. In this talk, we study the ill-posedness in the Besov space for one space dimension and in the Sobolev spaces for two space dimensions.

2012年06月08日(金)

GCOEレクチャーズ

14:00-15:30   数理科学研究科棟(駒場) 118号室
Mihnea Popa 氏 (University of Illinois at Chicago)
Derived categories and cohomological invariants II (ENGLISH)
[ 講演概要 ]
(Abstract for both Parts I and II)
I will discuss results on the derived invariance of various cohomological quantities, like the Hodge numbers, a twisted version of Hochschild cohomology, the Picard variety, and cohomological support loci. I will include a small discussion of current work on orbifolds if time permits.

Kavli IPMU Komaba Seminar

16:30-18:00   数理科学研究科棟(駒場) 002号室
Bong Lian 氏 (Brandeis University)
Period Integrals and Tautological Systems (ENGLISH)
[ 講演概要 ]
We develop a global Poincar\\'e residue formula to study
period integrals of families of complex manifolds. For any compact
complex manifold $X$ equipped with a linear system $V^*$ of
generically smooth CY hypersurfaces, the formula expresses period
integrals in terms of a canonical global meromorphic top form on $X$.
Two important ingredients of this construction are the notion of a CY
principal bundle, and a classification of such rank one bundles.
We also generalize the construction to CY and general type complete
intersections. When $X$ is an algebraic manifold having a sufficiently
large automorphism group $G$ and $V^*$ is a linear representation of
$G$, we construct a holonomic D-module that governs the period
integrals. The construction is based in part on the theory of
tautological systems we have developed earlier. The approach allows us
to explicitly describe a Picard-Fuchs type system for complete
intersection varieties of general types, as well as CY, in any Fano
variety, and in a homogeneous space in particular. In addition, the
approach provides a new perspective of old examples such as CY
complete intersections in a toric variety or partial flag variety. The
talk is based on recent joint work with R. Song and S.T. Yau.

2012年06月05日(火)

トポロジー火曜セミナー

16:30-18:00   数理科学研究科棟(駒場) 056号室
Tea: 16:00 - 16:30 コモンルーム
久野 雄介 氏 (津田塾大学)
A generalization of Dehn twists (JAPANESE)
[ 講演概要 ]
We introduce a generalization
of Dehn twists for loops which are not
necessarily simple loops on an oriented surface.
Our generalization is an element of a certain
enlargement of the mapping class group of the surface.
A natural question is whether a generalized Dehn twist is
in the mapping class group. We show some results related to this question.
This talk is partially based on a joint work
with Nariya Kawazumi (Univ. Tokyo).

GCOEレクチャーズ

16:30-18:00   数理科学研究科棟(駒場) 126号室
Yves Benoist 氏 (CNRS, Orsay)
Random walk on reductive groups II (ENGLISH)
[ 講演概要 ]
The asymptotic behavior of the sum of real numbers chosen independantly with same probability law is controled by many classical theorems: Law of Large Numbers, Central Limit Theorem, Law of Iterated Logarithm, Local Limit Theorem, Large deviation Principle, 0-1 Law,... In these introductory talks I will recall these classical results and explain their analogs for products of matrices chosen independantly with same probability law, when the action of the support of the law is semisimple. We will see that the dynamics of the corresponding action on the flag variety is a crucial tool for studying these non-commutative random walks.

Lie群論・表現論セミナー

16:30-18:00   数理科学研究科棟(駒場) 126号室
GCOE lectures
Yves Benoist 氏 (CNRS and Orsay)
Random walk on reductive groups (ENGLISH)
[ 講演概要 ]
The asymptotic behavior of the sum of real numbers chosen independantly with same probability law is controled by many classical theorems: Law of Large Numbers, Central Limit Theorem, Law of Iterated Logarithm, Local Limit Theorem, Large deviation Principle, 0-1 Law,... In these introductory talks I will recall these classical results and explain their analogs for products of matrices chosen independantly with same probability law, when the action of the support of the law is semisimple. We will see that the dynamics of the corresponding action on the flag variety is a crucial tool for studying these non-commutative random walks.

2012年06月04日(月)

代数幾何学セミナー

15:30-17:00   数理科学研究科棟(駒場) 122号室
渡辺究 氏 (埼玉大学)
Smooth P1-fibrations and Campana-Peternell conjecture (ENGLISH)
[ 講演概要 ]
We give a complete classification of smooth P1-fibrations
over projective manifolds of Picard number 1 each of which admit another
smooth morphism of relative dimension one.
Furthermore, we consider relations of the result with Campana-Peternell conjecture
on Fano manifolds with nef tangent bundle.

複素解析幾何セミナー

10:30-12:00   数理科学研究科棟(駒場) 126号室
濱野 佐知子 氏 (福島大学)
Log-plurisubharmonicity of metric deformations induced by Schiffer and harmonic spans. (JAPANESE)
[ 講演概要 ]
平面領域の Schiffer span および harmonic span は曲率負の距離を導くことを示し、複素パラメータ―を入れた複素2次元の空間が擬凸状の場合、ファイバーのそれらの距離は複素パラメータ―と共に対数的多重劣調和であることを示す。

2012年06月01日(金)

GCOEレクチャーズ

14:00-15:30   数理科学研究科棟(駒場) 118号室
Mihnea Popa 氏 (University of Illinois at Chicago)
Derived categories and cohomological invariants I (ENGLISH)
[ 講演概要 ]
(Abstract for both Parts I and II)
I will discuss results on the derived invariance of various cohomological quantities, like the Hodge numbers, a twisted version of Hochschild cohomology, the Picard variety, and cohomological support loci. I will include a small discussion of current work on orbifolds if time permits.

2012年05月31日(木)

統計数学セミナー

14:50-16:05   数理科学研究科棟(駒場) 006号室
参加をご希望される方は鎌谷 (阪大基礎工); kamatani at sigmath.es.osaka-u.ac.jpまでご連絡ください.
清 智也 氏 (慶應義塾大学 理工学部 数理科学科)
尤度計算のためのホロノミック勾配法 (JAPANESE)
[ 講演概要 ]
一般に,尤度関数に現れる正規化定数が解析的に求まらない場合,それを精度よく計算するには数値積分法や級数展開法を用いる必要がある.そして,いずれも多くの計算量を必要とする. 今回紹介するホロノミック勾配法は,ホロノミック性と呼ばれる良い性質を満たす関数に対し,関数値を複数の点(あるいは級数展開法では評価しにくい点)で計算する必要がある場合に,計算量の軽減が期待できる数値計算手法である. 特に,方向統計学に現れるFisher-Bingham分布族の正規化定数などは,ホロノミック性を満たすことを説明する. (参考文献:Nakayama et al. (2011), Adv. Appl. Math., 47 (3), 639--658. ほか)
[ 講演参考URL ]
http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2012/05.html

2012年05月30日(水)

代数学コロキウム

16:40-17:40   数理科学研究科棟(駒場) 056号室
Valentina Di Proietto 氏 (東京大学数理科学研究科)
Kernel of the monodromy operator for semistable curves (ENGLISH)
[ 講演概要 ]
For a semistable curve, we study the action of the monodromy operator on the first log-crystalline cohomology group. In particular we examine the relation between the kernel of the monodromy operator and the first rigid cohomology group, in the case of trivial coefficients, giving a new proof of a theorem of B. Chiarellotto and in the case of certain unipotent F-isocrystals as coefficients.
This is a joint work in progress with B. Chiarellotto, R. Coleman and A. Iovita.

講演会

14:50-16:20   数理科学研究科棟(駒場) 123号室
This is the fourth of four lectures planned on 5/25, 5/28, 5/29 and 5/30.
Harald Niederreiter 氏 (RICAM, Austrian Academy of Sciences)
Low-discrepancy sequences and algebraic curves over finite fields (III) (ENGLISH)
[ 講演参考URL ]
http://www.ms.u-tokyo.ac.jp/~matumoto/WORKSHOP/workshop2012.html

2012年05月29日(火)

トポロジー火曜セミナー

16:30-18:00   数理科学研究科棟(駒場) 056号室
Tea: 16:00 - 16:30 コモンルーム
中村 伊南沙 氏 (学習院大学,日本学術振興会)
Triple linking numbers and triple point numbers
of torus-covering $T^2$-links
(JAPANESE)
[ 講演概要 ]
The triple linking number of an oriented surface link was defined as an
analogical notion of the linking number of a classical link. A
torus-covering $T^2$-link $\\mathcal{S}_m(a,b)$ is a surface link in the
form of an unbranched covering over the standard torus, determined from
two commutative $m$-braids $a$ and $b$.
In this talk, we consider $\\mathcal{S}_m(a,b)$ when $a$, $b$ are pure
$m$-braids ($m \\geq 3$), which is a surface link with $m$-components. We
present the triple linking number of $\\mathcal{S}_m(a,b)$ by using the
linking numbers of the closures of $a$ and $b$. This gives a lower bound
of the triple point number. In some cases, we can determine the triple
point numbers, each of which is a multiple of four.

GCOEレクチャーズ

16:30-18:00   数理科学研究科棟(駒場) 126号室
Yves Benoist 氏 (CNRS, Orsay)
Random walk on reductive groups. (ENGLISH)
[ 講演概要 ]
The asymptotic behavior of the sum of real numbers chosen independantly with same probability law is controled by many classical theorems: Law of Large Numbers, Central Limit Theorem, Law of Iterated Logarithm, Local Limit Theorem, Large deviation Principle, 0-1 Law,... In these introductory talks I will recall these classical results and explain their analogs for products of matrices chosen independantly with same probability law, when the action of the support of the law is semisimple. We will see that the dynamics of the corresponding action on the flag variety is a crucial tool for studying these non-commutative random walks.

講演会

14:50-16:20   数理科学研究科棟(駒場) 123号室
This is the third of four lectures; the first is the colloquium on May 25th(Fri) 16:30--17:30 at 002 and the second is on May 28th(Mon).
Harald Niederreiter 氏 (RICAM, Austrian Academy of Sciences)
Low-discrepancy sequences and algebraic curves over finite fields (II) (ENGLISH)
[ 講演参考URL ]
http://www.ms.u-tokyo.ac.jp/~matumoto/WORKSHOP/workshop2012.html

2012年05月28日(月)

複素解析幾何セミナー

10:30-12:00   数理科学研究科棟(駒場) 126号室
田島 慎一 氏 (筑波大学)
Local cohomology and hypersurface isolated singularities II (JAPANESE)
[ 講演概要 ]
局所コホモロジーの孤立特異点への応用として
・$\mu$-constant-deformation の Tjurina 数
・対数的ベクトル場の構造と構成法
・ニュートン非退化な超曲面に対する Kouchnirenko の公式
について述べる.

代数幾何学セミナー

15:30-17:00   数理科学研究科棟(駒場) 122号室
Mihnea Popa 氏 (University of Illinois at Chicago)
Generic vanishing and linearity via Hodge modules (ENGLISH)
[ 講演概要 ]
I will explain joint work with Christian Schnell, in which we extend the fundamental results of generic vanishing theory (for instance for the canonical bundle of a smooth projective variety) to bundles of holomorphic forms and to rank one local systems, where parts of the theory have eluded previous efforts. To achiever this, we bring all of the old and new results under the same roof by enlarging the scope of generic vanishing theory to the study of filtered D-modules associated to mixed Hodge modules. Besides Saito's vanishing and direct image theorems for Hodge modules, an important input is the Laumon-Rothstein Fourier transform for bundles with integrable connection.

講演会

14:50-16:20   数理科学研究科棟(駒場) 123号室
This is the second of four lectures; the first is the colloquium on May 25th(Fri) 16:30--17:30 at 002.
Harald Niederreiter 氏 (RICAM, Austrian Academy of Sciences)
Low-discrepancy sequences and algebraic curves over finite fields (I) (ENGLISH)
[ 講演概要 ]
This is the second of the four lectures. The first one is Colloquium talk on May 25th 16:30--17:30 at 002.

Abstract from Colloquium:
Quasi-Monte Carlo (QMC) methods are deterministic analogs of statistical Monte Carlo
methods in computational mathematics. QMC methods employ evenly distributed
low-discrepancy sequences instead of the random samples used in Monte Carlo methods.
For many types of computational problems, QMC methods are more efficient than
Monte Carlo methods. After a general introduction to QMC methods, the talk focuses
on the problem of constructing low-discrepancy sequences which has fascinating links
with subjects such as finite fields, error-correcting codes, and algebraic curves.
[ 講演参考URL ]
http://www.ms.u-tokyo.ac.jp/~matumoto/WORKSHOP/workshop2012.html

2012年05月26日(土)

調和解析駒場セミナー

13:30-17:00   数理科学研究科棟(駒場) 128号室
このセミナーは,月に1度程度,不定期に開催されます.
河邑 紀子 氏 (University of North Texas) 13:30-15:00
The Takagi function - a survey (JAPANESE)
[ 講演概要 ]
More than a century has passed since Takagi published his simple example of a continuous but nowhere differentiable function,
yet Takagi's function -- as it is now commonly referred
to despite repeated rediscovery
by mathematicians in the West -- continues to inspire, fascinate and puzzle researchers as never before.
In this talk, I will give not only an overview of the history and known characteristics of the function,
but also discuss some of the fascinating applications it has found -- some quite recently! -- in such diverse areas of mathematics as number theory, combinatorics, and analysis.
寺澤 祐高 氏 (東京大学) 15:30-17:00
Dyadic, classical and martingale harmonic analysis II (JAPANESE)
[ 講演概要 ]
In a filtered measure space, we investigate the characterization of weights for which positive operators and maximal operators are bounded.

For this, a refinement of Carleson embedding theorem is introduced in this setting. Sawyer type characterization of weights for which a two-weight norm inequality for a generalized Doob's maximal operator holds is established by an application of our Carleson embedding theorem. If time permits, we would like to mention Hyt\\"onen-P\\'erez type sharp one-weight estimate of Doob's
maximal operator which is derived from our two-weight characterization.
This talk is based on a joint work with Professor Hitoshi Tanaka
(The University of Tokyo).

2012年05月25日(金)

談話会・数理科学講演会

16:30-17:30   数理科学研究科棟(駒場) 002号室
旧記録は、上記セミナーURLにあります。
お茶&Coffee&お菓子: 16:00~16:30 (コモンルーム)。

Harald Niederreiter 氏 (RICAM, Austrian Academy of Sciences)
Quasi-Monte Carlo methods: deterministic is often better than random (ENGLISH)
[ 講演概要 ]
Quasi-Monte Carlo (QMC) methods are deterministic analogs of statistical Monte Carlo methods in computational mathematics. QMC methods employ evenly distributed low-discrepancy sequences instead of the random samples used in Monte Carlo methods. For many types of computational problems, QMC methods are more efficient than Monte Carlo methods. After a general introduction to QMC methods, the talk focuses on the problem of constructing low-discrepancy sequences which has fascinating links with subjects such as finite fields, error-correcting codes, and algebraic curves.

This talk also serves as the first talk of the four lecture series. The other three are on 5/28, 5/29, 5/30, 14:50-16:20 at room 123.
[ 講演参考URL ]
http://www.ms.u-tokyo.ac.jp/~matumoto/WORKSHOP/workshop2012.html

GCOEレクチャーズ

14:00-15:30   数理科学研究科棟(駒場) 118号室
Mihnea Popa 氏 (University of Illinois at Chicago)
Generic vanishing theory and connections with derived categories (ENGLISH)
[ 講演概要 ]
I will give a basic introduction to the main results regarding the cohomology of deformations of the canonical bundle, and explain a connection with certain t-structures on the derived categories of Picard varieties. (This will also serve as an introduction for the talk at AG seminar on 5/28, 15:30-17:00.)

2012年05月23日(水)

PDE実解析研究会

10:30-11:30   数理科学研究科棟(駒場) 056号室
北海道大学のHPには、第1回(2004年9月29日)~第38回(2008年10月15日)までの情報が掲載されております。
Xingfei Xiang 氏 (East China Normal University)
$L^p$ Estimates of the Vector Fields and their Applications (ENGLISH)
[ 講演概要 ]
For $1< p < \\infty$, the estimates of $W^{1,p}$ norm of the vector fields in bounded domains in $\\mathbb R^3$ in terms of their divergence and curl have been well studied. In this talk, we shall present the $L^{{3}/{2}}$ estimates of vector fields with the $L^1$ norm of the $\\curl$ in bounded domains. By a similar discussion, we establish the $L^p$ estimates of the vector fields for $1 < p < \\infty$. As an application of the $L^p$ estimates, the Global $\\dv-\\curl$ lemma in Sobolev spaces of negative indices is given.

代数学コロキウム

16:40-17:40   数理科学研究科棟(駒場) 056号室
三井健太郎 氏 (東京大学数理科学研究科)
Simply connected elliptic surfaces (JAPANESE)
[ 講演概要 ]
We characterize simply connected elliptic surfaces by their singular fibers in any characteristic case. To this end, we study orbifolds of curves, local canonical bundle formula, and resolutions of multiple fibers. The result was known for the complex analytic case. Our method can be applied to the rigid analytic case.

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